CBSE Class 12 · 2006 · All India · Alternating CurrentShort Answer

An alternating voltage of frequency

f

is applied across a series LCR circuit. Let

f_{r}

be the resonance frequency for the circuit. Will the current in the circuit lag, lead or remain in phase with the applied voltage when
(i)

f > f_{r}

,
(ii)

f < f_{r}

? Explain your answer in each case.

Answer: (i) $f > f_{r}$ : current lags the voltage (inductive).
(ii) $f < f_{r}$ : current leads the voltage (capacitive).

Solution

Here

X_{L} = 2 π f L

grows with

f

while

X_{C} = \frac{1}{2 π f C}

falls with

f

; at

f = f_{r}

they are equal.
(i) For

f > f_{r}

X_{L} > X_{C}

, the net reactance is inductive, so the current lags the applied voltage.
(ii) For

f < f_{r}

X_{C} > X_{L}

, the net reactance is capacitive, so the current leads the applied voltage.

CBSE Class 12 Board · 2006 · All India · Subjective